Endogenous mobility, human capital and trade

Istvan Konya1

Boston College2

October, 2001

1I would like to thank Joseph Altonji, Kiminori Matsuyama, Yossef Spiegel andseminar participants at Boston College for helpful comments and suggestions.

2Correspondence: Istvan Konya, Department of Economics, Boston College.Tel (617) 552-3690. E-mail: konya@bc.edu

Abstract

The paper presents a model that can explain how regional differences emerge

in a country as a consequence of foreign trade. The model is based on the

widely used increasing returns/transportation costs framework. In addition

to the conventional elements, heterogeneous households and imperfect labor

mobility are added. The results indicate that for a small economy inter-

national trade leads to human capital reallocation, and thus more regional

inequality than without labor heterogeneity. Even small migration flows can

lead to large inequalities in per capita incomes, if the most skilled work-

ers move. The model also sheds some light on the relative importance of

fundamentals and historical factors.

Keywords: Migration, human capital, regional inequalities

JEL Classification: F12, R12, R23.

1 Introduction

Migration is an important mechanism in determining regional incomes. It

can act as a force of convergence between regions in neoclassical models,

and it can be a force for agglomeration if increasing returns are present. In

the age of mass migration wage inequality across the Old and New Worlds

decreased substantially because of the movement of labor, as Lindert and

Williamson (2001) documents. In models of agglomeration, however, migra-

tion of workers to urban centers leads to the emergence of regional inequalities

(Krugman 1991).

This paper is concerned with the inequality generating role of migra-

tion. In particular, I present a model in which migration acts as a powerful

magnification force that amplifies existing regional differences. It has been

documented by Gallup, Sachs and Mellinger (1998) that areas with good ac-

cess to transportation (coast lines, navigable rivers etc) are richer than other

regions. In a study of Japanese regions, Davis and Weinstein (2001) conclude

that locational fundamentals determine basic concentration patterns, but en-

dogenous agglomeration forces might play an important role in amplifying

these patterns. This paper is written in the same spirit, where a region with

a (potentially) small initial geographical advantage acquires a much bigger

lead in income through endogenous migration.

Regions differ in their access to outside markets, which gives the phys-

ically closer region a natural advantage. If the economy is closed, this ad-

1

vantage cannot be realized and spatial symmetry is an equilibrium. When,

however, the country opens up to international trade, the region closer to

the outside market will have a higher real wage and can potentially attract

immigrants from the other parts of the country. The crucial contribution of

the paper is to endogenize not just the size, but the composition of the mi-

gration flow. In particular, since migration costs are assumed to be the same

but labor market abilities are not, it will be the skilled workers who are most

likely to move. This has two consequences for regional inequalities. First,

the market size of the immigrant region will increase by more than the raw

number of immigrants, because their income and supply of efficiency units

of labor will be above average. In the presence of scale effects this leads to a

more than proportional increase in the wage rate. Second, average incomes

will be higher also because of the composition effect. The immigrant region

will have a distribution of skills skewed towards the highly skilled, whereas

the opposite is true for the other region. Thus the model’s prediction is that

migration of skilled people reinforces natural advantages by both the scale

and composition effects.

The example that motivated this research is the recent experience of

Hungary, where large income inequalities emerged in a short period of time

between seemingly very similar regions. Up to the end of the 1980s the Hun-

garian economy was a relatively closed one, at least to trade with the devel-

oped world. The reasons were mainly ideological, as the “socialist” countries

of Eastern Europe formed an autarchic trade block with the Soviet Union.

2

Since Hungary’s traditional trading partners are in Central and Western Eu-

rope, this arrangement (though providing some gains from specialization)

was largely artificial, and was only sustained by political means. In 1989,

when the Iron Curtain came down, Hungary liberalized its foreign trade in

a very short period of time. The old “socialist” trading block collapsed, and

in a few years Hungarian trade was redirected from Eastern Europe to the

West. It is natural that such a huge shock had a large effect on the coun-

try, above and beyond the shock of transforming a command economy into

a market economy. What is surprising is how different the response to these

shocks was in different parts of the country. Though the initial shock was

great in all regions, the northwestern counties rebounded fairly quickly, while

the eastern part still seems stuck in a deep recession.

It is interesting to contrast the experience of two counties: Gyor-Sopron-

Moson in the northwest corner and Borsod- Abauj-Zemplen in the northeast.

Though we do not have regional GDP measurement before 1994 in Hungary,

county level data on employment and industrial production are available.1

In 1989 industry employed about 15% of the population of both counties,

and the unemployment rates were practically zero. In the early 1990’s both

counties went into a deep recession, with many of the big state enterprises

struggling with the transition process. Since the middle of the decade, how-

ever, the two counties fared quite differently. In Gyor-Sopron-Moson indus-

1All the data in this paragraph comes from the Hungarian Statistical Yearbook 1989-1996.

3

trial production reached its 1989 level in 1996, and unemployment remained

around 6%. Industrial production stood at 62% of its 1989 level in 1996

in Borsod-Abauj-Zemplen, and the unemployment rate was close to 20%.

In 1997 per capita GDP was 60% higher in Gyor-Sopron-Moson than in

Borsod-Abauj-Zemplen. Did the emergence of such huge differences induce

emigration from the East to the West? Yes, but at a very modest level. Be-

tween 1989 and 1996 Gyor-Sopron- Moson saw a migration surplus of around

2% of its 1989 population, and Borsod-Abauj-Zemplen lost around the same

portion of its 1989 population to outmigration. Incentives to migrate were

clearly big, but the costs to do so were also fairly large.

The model presented in this paper can clearly explain these facts, be-

cause it focuses on the role of skilled people in the migration process. Even

if the migration flow is small, the resulting difference in average incomes can

be large, due to the scale and composition effects. In fact, the crucial role

is played by the latter, because even with small geographical differences it

can lead to large regional inequalities. On the other hand, the scale effect

is likely to be small when the underlying difference between regions is small,

so it is unlikely to explain the Hungarian story alone. In fact, wage rates

are not very different for comparable workers in the two regions (Magyar

Statisztikai Evkonyv [Hungarian Statistical Yearbook] 1989-1996). Evidence

from other countries underlines this pattern. In Britain, for example, Duran-

ton and Monastiriotis (2002) documents that regional inequalities arise from

differences in skill distribution, and not from differentials in wage rates.

4

The relevant literature for the paper is the “New Economic Geography”,

extensively discussed in Fujita, Krugman and Venables (1999). Models in

this tradition emphasize the role of endogenous forces (increasing returns

and pecuniary externalities) in creating agglomeration, as opposed to loca-

tional fundamentals.2 In Krugman (1991), the seminal article of the litera-

ture, agglomeration is a result of labor migration, but the only force creating

regional inequalities is the scale effect. Moreover, the model predicts large

population imbalances, which is not observed in the Hungarian example and

is unlikely to hold for European regions. The role of intermediate inputs in

creating industry linkages was emphasized in Krugman and Venables (1995),

which generates industrial agglomeration (and wage inequality) without mi-

gration. The problem with this approach – at least in the present context –

is that inequality results from wage differentials, and the composition effect

is absent, which seems empirically questionable. Second, the model predicts

complete industrial agglomeration in one region, which does not correspond

to the Hungarian experience.

While my specific example is Hungary, the point is much more general.

Examples such as the contrast between Northern and Southern Italy or the

differential development of the coastal and interior regions in China come

readily to mind. In general, it is usual to observe that a depressed region

first looses its most skilled workers, which further aggravates the problems.

2An exception is Matsuyama (1998), which has various core-periphery patterns emerg-ing as a consequence of geographical differences.

5

Also, attracting skilled people to a region is a first priority for regional plan-

ners. If we think that unemployment is concentrated among the less skilled,

the model can also explain why depressed region have much higher unem-

ployment levels (as we saw, this is the case in the Hungarian example). To

summarize, though my prime example and motivation is the Hungarian ex-

perience, the idea to introduce heterogenous workers into models of economic

geography is much more general and the model’s predictions can be applied

and tested in other countries as well.

The rest of the paper is organized as follows. Section 2 describes the

model. Section 2.1 outlines the main assumptions and analyzes household

and firm choices. Section 2.2 describes the goods market equilibrium condi-

tions, and Section 2.3 depicts the migration decision. In Section 3 the full

equilibrium of the model is described, with Section 3.1 containing results for

the autarchy two-region case. In Section 3.2 I introduce foreign trade into

the model and look at its effects on the two regions from. Section 3.3 dis-

cusses the role of expectations in the agglomeration pattern. Finally, Section

4 concludes.

2 The model

2.1 Basic assumptions

There are two countries, Home and Foreign, and Home has two regions,

East and West. The three regions can potentially trade with each other,

and goods are subject to transportation costs, which take the well-known

6

“iceberg” form.3 People can move between the East and West, but not

across borders. Migration is subject to a monetary cost of D, which can be

payed after moving. This amounts to the existence of perfect credit markets

that can finance the cost of relocation.

Consumers in any region consume a variety of goods. There are a contin-

uum of such goods, indexed from 0 to N . I assume that consumers maximize

the utility function

u =

[∫ N

0

c(i)1−1/σ di

] σσ−1

, (2.1)

where c(i) is consumption of good i, j is the index for households, N is the

measure of different products available (it will be determined endogenously)

and σ is the constant elasticity of substitution. Goods enter the utility func-

tion symmetrically, and consumers have a taste for variety4. For the chosen

market structure (see below) it is necessary to assume that σ > 1.

Although they have the same utility function, individuals have different

amounts of human capital. Household j has human capital hj, which it rents

out on the labor market. I assume that efficiency units of human capital

have a constant price w, thus household j receives an income of whj. Then

the budget constraint can be written as∫ N

0

p(i)cj(i)di = whj, (2.2)

with p(i) standing for the price of good i. From (2.1) and (2.2) we can cal-

3If τ > 1 units of a good are shipped from region i, only 1 unit arrives in region j.4This can be seen by setting c(i) = c/N , and noticing that the resulting expression is

increasing in N , the measure of variety.

7

culate the demand function of person j for good i. As (2.3) below shows,

demand is linear in human capital. Aggregation is thus an easy task, and ag-

gregate demand in a region for good i is given by (2.4), where H is aggregate

human capital in the region5

cj(i) =

[p(i)

P

]−σwhj

P(2.3)

c(i) =

[p(i)

P

]−σwH

P. (2.4)

P is the true price index in the region, and it is given by the following

expression:

P =

[∫ N

0

p(i)1−σdi

] 11−σ

. (2.5)

Now we can turn to firms. Since they are infinitesimal, they can only set

their own price and their decision does not affect the aggregate price index.

Production input takes the form of efficiency units of human capital. In order

to produce, a firm must pay a variable cost of βw per unit of output and a

fixed cost of αw. Thus the cost function has the following form:

TC = (α + βq)w, (2.6)

where q is the quantity produced by the firm6. Firms take the regional

demands as given in (2.4). In principle they could charge different prices for

different regions. In turns out, however, that it is optimal to set the same

5For now I omit regional indexes, since the equations so far apply to every regionseparately. But notice that prices, wages, the range of goods and aggregate human capitalare all region specific, and will be treated as such when necessary.

6When no confusion arises, I omit the product index i.

8

price for every region. Assuming that there are no arbitrage possibilities in

trade guarantees that if a firm sets a price of p(i) for its export good, it will sell

in the destination market for τp(i), where τ is the “iceberg” transportation

cost. But if we substitute this into the regional demand function, it will have

the form of kp(i)−σ, where k is a constant from the firm’s point of view.

Since the transportation cost is a part of only k and the profit maximizing

price only depends on the constant elasticity of substitution σ, the firm will

set the same price of its good for all regions.

Formally, substitute kp(i)−σ for q(i) into pq−TC, rearrange the first-order

condition to get

p(i) =σ

σ − 1βw. (2.7)

This is the well-known result that firms apply a constant markup over mar-

ginal cost that is a decreasing function of the demand elasticity. The optimal

price is the same for all regions, and it is also independent of the index i, since

goods are completely symmetric. We can count the goods on an arbitrary

scale, so I set units in such a way that βσ/(σ − 1) = 1, to simplify notation.

There are no barriers to entry by additional firms. Since firms are in-

finitesimal, entry continues until it drives profits to 0. The zero profit condi-

tion pins down firm size:

q = ασ, (2.8)

after using the normalization β = (σ− 1)/σ. Finally, factor markets clear in

9

all regions. Using (2.8) and σ/(σ − 1)β = 1, we have that for region m

Hm = Nm(α + βq) = Nmασ.

Rearranging for Nm we find that the number of firms in region m is given by

Nm =Hm

ασ. (2.9)

2.2 Equilibrium on the goods market

In the full equilibrium of the model both wages and the distribution of human

capital are endogenous. To solve the model, I first write down the equilibrium

condition on the market for goods with a given distribution of human capital.

Then I will use the equilibrium wage rate in the migration decision to close

the model.

Since all varieties produced in a country have the same price and demand

for them is symmetric, there will be only as many market clearing equations

as countries. The supply of a variety is given by (2.8), this must be equal

total demand in the regions, each given by (2.4). Notice that we can simplify

the price index Pm, since all varieties from country k have the same price, so

that

P 1−σm =

∑k

Nkw1−σk .

Next, we can use (2.9) that links the number of varieties produced in a

region to the aggregate level of human capital there, and substitute it into the

price index term. Using the result in the demand functions, the equilibrium

10

condition for a variety produced in region m can be written as∑k

τ 1−σmk w−σ

m wkHk∑j τkjw

1−σj Hj

= 1. (2.10)

It must be noted that one of the equations is redundant by Walras’ Law,

since only relative prices matter. Thus we will normalize one wage rate in

what follows, setting ww = 1, we = w and wf = v.

2.3 The migration decision

I assume that the initial position is when the East and West are completely

symmetric in their size and distribution of human capital endowments. Given

the symmetry of the problem, I will only look at the possibility of migration

from the East to the West. Person j moves if her utility is greater in the

West. Given migration costs, her nominal income is hj − D in the West

and whj in the East. With homothetic preferences utility is proportional to

the real wage, where the deflator is the price index. Thus the condition for

moving is given by

hj −D

Pw

>whj

Pe

⇒ hj

(1− wPw

Pe

)> D.

Notice that if it is profitable for person j to move, all other workers with

human capital greater than j will move as well. This is because the gain

from moving is linear in hj for individuals, since their isolated actions do not

influence the wage rate and the migration cost is constant. Also, because

the wage rate will be bounded form below, gains from migration are finite.

Thus assuming there are people with very low levels of human capital, there

11

will always be someone for whom moving is not profitable. To assure that, I

assume that hj ∈ [0, 1], with full support.7

That means that if there is migration in equilibrium, there must be a

marginal person who is indifferent between migrating or not. Let the human

capital level of that person be x. Then every worker who has hj > x will

migrate, and all the others will stay. Thus the migration equilibrium of the

model can be written as

x

(1− wPw

Pe

)≤ D and x ≤ 1, (2.11)

with complementary slackness.

Of course in equilibrium the wage rate and the price index depend on the

distribution of human capital, and hence on x. For future reference let us

define

B(x) ≡ x

[1− wPw

Pe

(x)

],

which gives the gains from migration for the marginal person who is indif-

ferent between moving and staying. Thus equilibrium is given by B(x) ≤

D, x ≤ 1. It is important to understand that B(x) is an aggregate function,

and does not correspond to individual gains from moving.

3 The impact of international trade

The full equilibrium of the model is characterized by the wage rates in the

regions, and the distribution of human capital between the East and West,

7This assumption is not essential, but simplifies the analysis by ruling out full agglom-eration.

12

given that the starting position is full symmetry between these two regions.

The wage rates can be calculated from the market clearing conditions (2.10),

which also determine the price indexes. Then the distribution of human

capital must adjust to satisfy (2.11). Although we are interested in the effect

of trade with Foreign, it is instructive to understand how the model works

in the closed economy. Let us start with that case.

3.1 Two regions

In this case the market clearing conditions can be written in more simpler

forms. Let ρ = τ 1−σew . Using (2.10), we can write the two equations as

Hw

Hw + ρw1−σHe

+ρwHe

ρHw + w1−σHe

= Hw + He

ρw−σHw

Hw + ρw1−σHe

+w1−σHe

ρHw + w1−σHe

= Hw + He.

We can further simplify the equilibrium condition (the two equations are not

independent) by multiplying the first equation by ρw−σ and substracting it

from the second. This yields the following equation:

w1−σ − ρw

wσ − ρ=

Hw

He

. (3.1)

It is easy to check that there is a unique positive solution to the equation,

with wσ ∈ [ρ, 1/ρ]. The equilibrium relative wage in the East is a decreasing

function of Hw/He and it increases with the ease of transportation, ρ if and

only if w ≤ 1.

13

Next, we can use (3.1) to simplify wPw/Pe. Combining it with the defi-

nitions of the price indexes, we get

wPw

Pe

= w2σ−1σ−1 . (3.2)

Thus the migration gain function can be written in this case as

B(x) = x[1− w(x)2σ−1σ−1 ]. (3.3)

Finally, aggregate human capital levels are characterized by

He =

∫ x

0

h dG(h)

Hw =

∫ 1

0

h dG(h) +

∫ 1

x

h dG(h). (3.4)

The full equilibrium of the model is given by (3.1), (2.11) together with (3.3)

and (3.4).

We can easily check that no migration is an equilibrium. In such a sit-

uation Hw/He = 1, w = 1, B(x) = 0 and hence x = 1. Moreover, it is

“tatonnement” stable, since a small deviation will lead to migration gains

smaller than the migration cost D, as long as D > 0. The more interesting

question is whether there exists another stable equilibrium with positive mi-

gration. Proposition 1 shows that the answer is affirmative, as long as the

migration cost is not too high.

Proposition 1. For low enough migration costs there exist a stable equilib-

rium with positive migration flows.

14

Proof. The following properties of B(x) can be shown easily: B(1) = B(0) =

0, B′(0) > 0 and B′(1) < 0. The last two can be seen from the following:

B′(x) = 1− w2σ−1σ−1 − 2σ − 1

σ − 1w

σσ−1 w′(x),

and from the fact that w′(x) > 0. By the continuity of B the derivative

properties also extend to neighborhoods of the two endpoints. Stability re-

quires that at the equilibrium point B′ > 0, and it follows that we can find

a small enough D that intersects the B schedule at its increasing part close

to x = 0.

There is a presumption that B(x) is quasi-concave, in which case there is a

unique stable interior equilibrium (and also an unstable one). The restriction

needed is that the p.d.f. g(h) does not decrease too fast at any interior point

where B′(x) = 0.8 In the heuristic discussions below I will assume that is

the case.

Figure 1 depicts the determination of the equilibrium with ρ = 3/4,

σ = 2 and G(h) = h.9 If the moving cost is in the appropriate range we have

multiple equilibria. Even if initially the regions are perfectly symmetric,

if many people think that moving is profitable inequalities emerge. Thus

expectations have an important role in generating regional inequalities in a

closed economy. Moreover, as we can see from the picture, moving involves

a large shift in population. This result follows from the structure of the

8A function f(y)is quasi-concave at y0 iff for any y such that yf ′(y0) = 0 we havey2f ′′(y0) ≤ 0. This condition is satisfied at any point x where B′(x) 6= 0. When B′ = 0,B(x) needs to be concave, which can be guaranteed by the above condition.

9In this case E(h)=1/2.

15

0

0.1

0.2 0.4 0.6 0.8 1

x

Figure 1: Equilibrium in a closed economy

model, since in order to get sufficient difference in real wages, there must

be a large flow of immigration. If the symmetric equilibrium is the initial

situation, there must be a dramatic shift in expectations for the asymmetric

equilibrium to emerge, even when migration costs are low enough. Thus it

seems fair to conclude that although a migration equilibrium is possible, the

symmetric one is stable not just locally, but in a neighborhood with positive

measure. Thus when introducing foreign trade I start from a position of

symmetry.

16

3.2 Three regions

Now we can turn to the question of how opening the country to foreign

trade changes the equilibria. For simplicity I treat the outside region as a

homogenous unit, within which trade is costless. I’ll label the foreign region

with subscript f . To emphasize the difference in the distances from the

outside region, I will use the following linear geographic structure shown

below:

f w e

� -µ � -τ

The picture shows that transport costs are µ between the world and West and

τ between East and West. Then a natural assumption is that the transport

cost between Foreign and East is µτ . This assumption lets us reduce the

number of distance parameters to two, and given the nature of the question,

a natural one to make.

Let us proceed with the equilibrium conditions on the goods market.

The pricing equations and the equilibrium scale of production are still given

by (2.7) and (2.8). Similarly, for each region the number of firms will be

proportional to the amount of human capital, ασNl = Hl for region l. Using

17

the additional notation θ = µ1−σ, we can write the price indexes as follows

ασP 1−σe = ρHw + w1−σHe + ρθv1−σHf

ασP 1−σw = Hw + ρw1−σHe + θv1−σHf (3.5)

ασP 1−σf = θHw + ρθHe + v1−σHf ,

where Hf is the (exogenous) size of the foreign country, and v is the wage

rate prevailing in the foreign country. Then the equilibrium conditions for a

given distribution of human capital are written as

ασ(Hw + He + Hf ) =ρw−σHw

P 1−σw

+w1−σHe

P 1−σe

+ρθw−σvHf

P 1−σf

ασ(Hw + He + Hf ) =Hw

P 1−σw

+ρwHe

P 1−σe

+θvHf

P 1−σf

(3.6)

ασ(Hw + He + Hf ) =θv−σHw

P 1−σw

+ρθv−σwHe

P 1−σe

+v1−σHf

P 1−σf

.

These equations (of which only two are independent) do not seem to

yield analytical results easily, but it turns out that one can characterize the

equilibrium in every important aspect. After some algebraic manipulations10,

we can characterize the solution by the following two equations:

Hw + θv1−σHf =w1−σ − ρw

wσ − ρHe

Hw + ρw1−σHe =v1−σ − θv

vσ − θHf .

10Substitute the price index definitions from (3.5). Multiply the second equation byρw−σ and subtract it from the first, this leads to (3.7). Then multiply the second equationby θv−σ and subtract it from the third, which leads to (3.8).

18

The equations are scale free, so we can introduce the new variables h =

Hw/(He + Hw) and hf = Hf/(He + Hw) to get

h + θv1−σhf =w1−σ − ρw

wσ − ρ(1− h) (3.7)

h + ρw1−σ(1− h) =v1−σ − θv

vσ − θhf . (3.8)

The equilibrium wage rates w and v are thus the solutions to (3.7) and (3.8).

0

0.1

0.2 0.4 0.6 0.8 1

x

Figure 2: The effect of trade on a large country

Appendix A shows that there is a unique solution to the above system.

Moreover, it is possible to show that Pw/Pe takes the same form as in the

19

previous section, thus (3.3) continues to hold.11 Thus the equilibrium condi-

tions in the three region case are given by (3.7), (3.8), (2.11) together with

(3.3) and (3.4). Proposition 2 summarizes the main result of this section.

Proposition 2. If migration costs are high, the symmetric equilibrium is

stable. For low migration costs, symmetry must be broken, and there exists

at least one stable interior equilibrium.

Proof. Appendix A shows that the equilibrium Eastern wage is decreasing

in h, the share of the West in Home’s human capital. Moreover, from (3.7)

it follows that

w = 1 ⇒ h =1− θv1−σhf

2<

1

2.

These together imply that

h =1

2⇒ w < 1 ⇒ B(1) > 0.

Thus for low enough migration costs, symmetry is no longer an equilibrium.

Since B(0) = 0, if symmetry is broken, there must exist at least one stable

interior equilibrium.

Figure 2 and Figure 3 show what happens with the migration gain func-

tion B(x) when a country opens up to international trade. The parameter

values ρ = 3/4, θ = 1/2, σ = 2 and G(h) = h are common in both figures,

but the first one uses hf = 1/2 and the second uses hf = 5. The pictures

confirm that low migration costs lead to symmetry breaking in this model.

11Solve (3.7) and (3.8) for h and hf and substitute these into the price indexes.

20

0

0.2

0.2 0.4 0.6 0.8 1

x

Figure 3: The effect of trade on a small country

More interestingly, as the relative size of the outside region increases, the

decreasing portion of the gains function disappears. This is a direct con-

sequence of the comparative statics result proved in Appendix B, that w

decreases with hf . This has two consequences. First, small or undeveloped

countries are more likely to experience migration as a consequence of trade.

Second, observed migration flows are likely to be smaller on average in small

countries. In small countries the migration level is a continuous function of

migration costs, as Figure 3 shows. In large countries, on the other hand,

the migration level jumps from zero to a large fraction when the migration

21

cost falls below B(1) (assuming that in case of multiple stable equilibria the

symmetric one is selected). Thus, according to the model, small countries

will be more likely to experience trade induced migration, but the resulting

asymmetry will be smaller than in large countries with a migration equilibria.

Before finishing this section, it is worth evaluating a quantitative exam-

ple about the effects of migration on regional incomes. In the introduction I

stated that high-skilled migration has a scale effect and a composition effect

(in addition to the market access effect that arises purely from geographical

differences). The first leads to higher wages in the West per unit of effective

labor, and the second leads to higher human capital per capita. To quantify

these two effects, let us assume that in equilibrium 5% of the East’s popu-

lation migrates to the West. Assuming σ = 4, ρ = 3/4 (τ = 1.1), θ = 1/2

(µ = 1.26) and hf = 5, without migration the Eastern real wage relative to

the Western real wage would be wPe/Pw = w2σ−1σ−1 = 0.9 (the market access

effect). With migration and thus a change in the human capital levels, and

assuming G(h) = h, wPe/Pw = 0.898 (the scale effect). Thus the scale ef-

fect due to skilled migration is quite small. The composition effect, however,

is large. Average human capital in the East relative to the West drops to

(1 − h)/h = 0.82, which leads to a relative average income in the East of

0.736. Thus increasing returns themselves do not magnify significantly the

geographycal disadvantage of the East (the real wage difference is essentially

the same as the transportation cost between the East and the West), the

composition effect adds an additional 17% to regional inequalities.

22

This calculation was made for a small economy (hf = 5), let us redo it

for a large country, assuming hf = 1. Without migration, the real wage ratio

would be 0.951. Adding migration decreases the relative Eastern real wage

to 0.941. Assuming the same level of migration, the composition effect is the

same, (1− h)/h = 0.82. The total effect is, then, 0.77. Thus opening up has

a smaller effect on a larger country (keeping the level of migration constant),

but the scale effect is larger. This follows from the fact that larger countries

rely less on international trade, so the internal market is more important. In

contrast, outside market access is more crucial for small economies, so the

total effect will be larger.

3.3 History vs. expectations

In the previous section I focused on equilibria when migration flows from

the East to the West. In principle, however, it is possible that despite the

natural advantage of the West, there exists a stable equilibrium with people

moving to the East. Intuitively, since in autarchy there is a stable equilibrium

with such property (as long as migration costs are not very large), if the

geographical advantage of the West is small, such an equilibrium might be

preserved in free trade. In this section I investigate under what parameter

values expectations might lead to this “unhistorical” outcome.

According to (3.3) gains from migration depend only on the equilibrium

wage rate in the East for the marginal migrant. Thus in order to have an

equilibrium with migration to the East, we need w > 1. The previous section

23

showed that this is possible if

h >1− θv1−σhf

2,

where v is determined by (3.8). Migration to the East is a possible equilib-

rium if (w = 1, v > 0) solves (3.7) and (3.8) for 0 < h ≤ 1/2.

This suggests that we can calculate a cutoff in the parameter values that

separate the states of nature when migration to the East is possible from

when it is not. Such a cutoff might be given for hf , the relative size of

Foreign. The reason is that w is decreasing in hf , as Appendix B shows. To

calculate the cutoff, we can solve (3.7) for v at w = 1, h = 1 and then solve

(3.8) for hf . Migration to the East is a possible equilibrium if

hf <1

θ

[1 + ρ2

θ(1 + ρ)

]1−1/σ

≡ hf ,

where the right-hand side is decreasing in both θ and ρ. For the parameter

values used for the previous simulations (ρ = 3/4, θ = 1/2 and σ = 2), the

cutoff is hf = 2.33. It is easy to see that hf > 1, so that for a large country

reverse migration is always possible. For small and/or underdeveloped coun-

tries, however, the direction of migration is determinate: it has to flow from

the East to the West. Thus in these economies expectations have no role in

determining the equilibrium outcome.

A related question concerns the effect of international trade on an asym-

metric situation where the agglomeration is in the East. The above analysis

shows that for hf > hf the equilibrium wage rate in the East is always smaller

than the wage rate in the West, so that there are incentives to migrate. Even

24

if hf < hf , for 0 << h < 1/2 the model predicts w < 1. Thus when migration

costs are low enough, Home is likely to experience a complete reversal of ag-

glomeration patterns. Thus the model can provide an alternative rational to

the experience of Mexico - freer trade led to a reallocation of manufacturing

from Mexico City to the northern border region - to that found in Krugman

and Livas (1996). It is unlikely, of course, that Mexico City will loose its

prominence completely, since it has advantages not captured in this model.

Nevertheless, I believe that the current model presents a more plausible story

about the rise of Mexico’s border region. After all, the new agglomeration

emerged not just anywhere, as Krugman and Livas (1996) suggests, but next

to the US border. Thus geography is clearly important in explaining location

patterns, and the model in this paper shows the fruitfulness of exploring the

complementarities between location and increasing returns.

4 Conclusion

In this paper I presented a model in which international trade can cause sub-

stantial regional differences in a country, even if there were none before trade

liberalization. The main driving forces are the possibility of migration, trans-

portation costs, increasing returns and the heterogeneity of the population

with respect to human capital. While the first three elements are conven-

tional in models of the ”New Economic Geography”, heterogeneity (to the

best of my knowledge) is a novel feature. Although in general it poses sub-

stantial difficulties to solve the model with heterogenous agents, with some

25

simplifying assumptions we were able to get interesting and plausible results.

The main conclusion of the model is that migration is a powerful ampli-

fying force of regional inequalities, if it involves the most skilled. Regional

inequalities can emerge within a closed country in some cases as self-fulfilling

expectations, and they are inevitable in a small open economy. As a result,

average incomes differ sharply, even if migration flows are small, because of

the human capital reallocation (composition) effect. Finally, fundamentals

matter more than history in a small open economy with a mobile popula-

tion, as the geographically disadvantaged region cannot maintain its earlier

agglomeration advantage.

Admittedly the model presented in this paper is very specific. There is

only one sector using one factor, and the assumed distribution of human

capital is not very realistic. Nevertheless, I believe the model has general

implications. It shows us that incorporating heterogeneity into economic

geography models is fruitful and important. With heterogenous workers we

can understand why depressed regions can form rapidly and why it is difficult

to improve their situation. The model also shows that even small geographic

differences can lead to large inequalities, without much agglomeration or

concentration. The challenge for future research is to build more general

models of economic geography with heterogeneity, introduce dynamics and

provide more analytical results. I hope that this paper is a step in this

direction.

26

References

Davis, D. R. and Weinstein, D. E. (2001). Bones, bombs and break points:

the geography of ecnomic activity, Working Paper 8517, NBER.

Duranton, G. and Monastiriotis, V. (2002). Mind the gaps: the evolution of

regional earnings inequalities in the UK 1982-1997, Journal of Regional

Science. Forthcoming.

Fujita, M., Krugman, P. and Venables, A. J. (1999). The Spatial Economy,

The MIT Press, Cambridge MA.

Gallup, J. L., Sachs, J. D. and Mellinger, A. D. (1998). Geography and

economic development, Working Paper 6849, NBER.

Krugman, P. (1991). Increasing returns and economic geography, Journal of

Political Economy 99: 483–499.

Krugman, P. and Livas, R. E. (1996). Trade policy and the third world

metropolis, Journal of Development Economics 49: 137–150.

Krugman, P. and Venables, A. J. (1995). Globalization and the inequality of

nations, The Quarterly Journal of Economics 110(4): 857–880.

Lindert, P. H. and Williamson, J. G. (2001). Does globalization make the

world more unequal?, Working Paper 8228, NBER.

Magyar Statisztikai Evkonyv [Hungarian Statistical Yearbook] (1989-1996).

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27

Matsuyama, K. (1998). Geography of the world economy, Northwestern Uni-

versity.

Appendix

A The existence of equilibrium with three re-

gions

Let us rewrite the equations that define the equilibrium wage rates from (3.7)

and (3.8):

A(v, w) ≡ h + θv1−σhf −w1−σ − ρw

wσ − ρ(1− h) = 0 (A.1)

B(v, w) ≡ h + ρw1−σ(1− h)− v1−σ − θv

vσ − θhf = 0. (A.2)

The two equations implicitly define two relationships between w and v, and

their intersection determine w and v. There is a unique and stable (in the

tatonnemant sense) equilibrium if

−Av

Aw

< −Bv

Bw

⇔ −Av

Bv

< −Aw

Bw

.

To prove that this holds, it is sufficient to show that −Av < Bv and Aw >

−Bw. I will only derive the first of these results, since the second one can be

shown completely analogously.

Bv + Av =[(σ − 1)v−σ + θ](vσ − θ) + σvσ−1(v1−σ − θv)

(vσ − θ)2hf − (σ − 1)θv−σhf

=(σ − 1)[1− θvσ + (1− θv−σ)(1− θvσ + θ2)] + 1− θ2

(vσ − θ)2hf

> 0,

28

since vσ ∈ [θ, 1/θ]. Thus the equilibrium wage rates are unique.

B Comparative statics with three regions

Let ∆ = AvBw − BvAw, which was shown to be positive in the previous

section. Using this, it is easy to prove some comparative statics results for

w:

dw

dh=

1

∆(BvAh − AvBh) =

1

∆

[Bv

(1 +

w1−σ − ρσ

wσ − ρ

)− Av(1− ρw1−σ)

]< 0

dw

dθ=

1

∆(BvAθ − AvBθ) =

h2fv

1−σ

∆(vσ − θ)2[2(1− σ)(1− θv−σ)− (1− θ2)] < 0

dw

dhf

=1

∆(BvAhf

− AvBhf) = −θσv1−σhf (1− θ2)

∆(vσ − θ)2< 0

The effect of ρ is in general ambiguous.

29